Web: http://arxiv.org/abs/2201.12212

Jan. 31, 2022, 2:11 a.m. | Thomas W. Mitchel, Noam Aigerman, Vladimir G. Kim, Michael Kazhdan

cs.LG updates on arXiv.org arxiv.org

M\"{o}bius transformations play an important role in both geometry and
spherical image processing -- they are the group of conformal automorphisms of
2D surfaces and the spherical equivalent of homographies. Here we present a
novel, M\"{o}bius-equivariant spherical convolution operator which we call
M\"{o}bius convolution, and with it, develop the foundations for
M\"{o}bius-equivariant spherical CNNs. Our approach is based on a simple
observation: to achieve equivariance, we only need to consider the
lower-dimensional subgroup which transforms the positions of points as …

arxiv cnns cv

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